Simplify. Rewrite the expression in the form $y^n$. $y^6\cdot y^3=$
$\begin{aligned} y^6\cdot y^3&=y^{6+3} \\\\ &=y^{9} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} y^6\cdot y^3&=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y}_\text{6 times}\cdot\underbrace{y\cdot y\cdot y}_\text{3 times} \\\\\\ &=\underbrace{y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y\cdot y}_\text{9 times} \\\\ &=y^{9} \end{aligned}$ In conclusion, $y^6\cdot y^3=y^{9}$.